The Doncaster 22-year-old led with five seconds to go but saw glory snatched away from him by Uzbekistan’s Ulugbek Rashitov who produced a late head kick to turn the match around and win 34-29.
Sinden wins the silver, Britain’s first of these Games, and adding to the bronze won earlier by Chelsie Giles in the judo.
Rashitov, 19, was 13-8 ahead after the first round but Sinden reduced the deficit to 18-14 at the end of the second.
The third and final round was impossibly dramatic as the lead changed hands several times and Sinden led 28-26 with seconds remaining only for Rashitov to land a turning kick and then another kick to the body in the closing stages to win the contest.
"The feeling right now is just disappointment, it was my gold medal to give away and it's a hard one to take," said Sinden.
"I'm gutting and hard when you get silver, when you win gold or bronze you get to celebrate but you don't with silver.
"I'll reflect on this and be proud of what I've achieved in these last five years, from having no ranking points to becoming world champion and winning an Olympic silver.
"It was my gold medal to give away - obviously he is a good fighter, I just made a few mistakes. I think I got unlucky with a few things as well but that is taekwondo.
"I knew what time was left and I thought I was controlling it well but he reacted well and caught me.
"I thought he was on the back foot. You have to commend him for what he did - a few mistakes from me, well done to him."
Sinden is already eyeing going one better at the 2024 Olympic Games in France.
He added: "You'll see me again in Paris, I'm just getting started. Sometimes you learn more than defeats and I'll be taking that learning curve into Paris and hopefully I can go one better."
Sinden’s silver medal followed a shock first-round loss for double defending champion Jade Jones, whose hopes of becoming the first British woman to win golds at three consecutive Games were ended in a 16-12 defeat to Refugee Team athlete Kimia Alizadeh.
Sinden, who won the world title in Manchester in 2019, had cruised through his two opening contests, compiling a total of 92 points in wins over New Zealand’s Tom Burns and Hakan Recber of Turkey.
He then beat China’s Zhao Shuai in the semi-final to secure his place in the gold medal match.
Earlier Jones, 28, who had ended a long wait for her first world title in 2019, led early against Alizadeh but could not make her advantage count and fell to a disappointing defeat.
For an opening bout it was as tough as they come against Alizadeh, who became the first Iranian woman to win an Olympic medal when she took bronze in Rio behind Jones.
Alizadeh, also a two-time world medallist who beat Jones in the 2015 event in Russia, subsequently left her homeland to train in Germany, a decision which led to a period of inactivity that meant she was not seeded in the women’s -57kg category.
Any hopes Jones may have had of challenging for a bronze medal via the repechage were ended when Alizadeh was subsequently beaten in her semi-final match by Tatiana Minina of Russia.